It's the new must-have accessory for the French schoolchild who is already equipped with the requisite Nike trainers, Lacoste sweatshirt and Hilfiger baggies: "bully insurance", in case some or all of the above get nicked.

Inspired by a sharp increase in school violence, several insurance companies have launched policies covering everything from stolen textbooks to ripped clothing.

"It was the families who started asking us to come up with something," said Patrick Moreau of the insurance company MEA.

"They are fed up with their kids coming home minus some very expensive piece of designer gear."

All parents of French schoolchildren pay a compulsory student insurance premium that starts at about £5 a year to cover accidents such as broken bones or smashed spectacles. The bully insurance is an optional top-up policy covering theft or deliberate damage.

School violence, racketeering and bullying have become a growing concern in recent years, reflecting a steady increase in overall crime rates that politicians from all main parties have identified as the main campaign issue for next year's parliamentary and presidential elections.

Adolescent brutality is now a serious problem in many schools, particularly in the suburbs of large cities. Three middle school students were recently accused of attempted murder after throwing an 11-year-old over a railing. In another case, a 14-year-old technical school student told a court that for 18 months a group of classmates had burned him with soldering irons and cigarettes.

For the first time in France, some 20 schools in the greater Paris area will next week open their doors equipped with CCTV cameras to record all assaults and threatening behaviour, and hopefully serve as a deterrent to would-be bullies.

"The whole phenomenon is worrying in the extreme," Jack Lang, the education minister, said this week. He outlined new measures to combat aggression, such as a national publicity campaign in all schools, fresh guidelines for teachers and a special computer program to keep track of violent incidents and the pupils involved in them.

Police say there were 30,000 serious cases of bullying reported last year, often after children were attacked for refusing to hand over a prized piece of designer gear.

The insurers expect most claims to involve similar incidents, although they will also pay out for medical treatment if a child is injured by bullies at school or on the way there. The only material losses they will not reimburse are cash and mobile phones.

Not all parents, however, are convinced. "I'm not sure I would go to the police to report a stolen pair of trainers and then try and claim back what they cost from an insurance company," Antoinette Guérin, the mother of a 12-year-old boy in Paris's ninth arrondissement, said.

"I think I'd be far more concerned about helping to repair the psychological damage, the stress and the humiliation. Material objects can always be replaced."